Re: [tuning] A Young Person's Guide to Music and Number

Thanks, Yahya,

It's always good to get a rethink of what I'm after.

I only skimmed the harmonograph thread, but I'll look at it again.

The audience I intend to address (for now) would hopefully be a cross-section of teaching professionals (from as many fields as I could entice with a catchy title, which is not the subject line here!), psychologists/counselors, etc. and university students. My experience has been that it's the singers who are the most recalcitrant when it comes to theory, and especially math. ;-) (Sorry...)

Better questions to you and the group, for my purposes, might be,

1.) "When and how (!) did the relationship of music to numbers-or vice versa- become meaningful to you?" (if it did... :-)

2.) "As a mathematically or technically inclined person, what, if anything, have you felt to be an unfortunate oversight in your musical education?"

Or the reverse of that,

3.) "As a musically inclined person, ...in your mathematical/technical education?"

Many of the American students I've observed in World Music classes find the music of other cultures "irritating" or "boring", especially the further one gets from any kind of western pop-music "fusion". (My own feelings are pretty much the opposite, the less like western music it sounds, the happier I am to listen to it! So to speak...)

In any case, it seems to me that early exposure to different musical practices would help to make it easier for an opera singer to listen to Indian classical music, for example. (Or, in my case, for rock 'n' roller to listen to, say, Schubert.)

But, I'm really trying to address issues of creativity and individuality/originality, so as to encourage both as means to better overall education. In the present educational environment [in California, at least] I think a large scale disaster is most often frightfully exacerbated by official policy.

Of course, this may only be my unfortunate opinion, and in fact the system will be wildly successful, once _all_ artistic considerations are weeded out.

;-)

Regards,

Pete

Yahya Abdal-Aziz <yahya@melbpc.org.au> wrote:

-----Original
Message-----________________________________________________________________
________
Date: Fri, 11 Mar 2005 00:24:29 -0800 (PST)
From: Pete McRae
Subject: Re: A Young Person's Guide to Music and Number (was CD Sales...)

...

[Pete]
I'm presently really trying hard to brainstorm a Senior Project for a Music
Ed. degree, that could take a more rigorous (?) pedagogical approach to
music and number, for high school (and elementary school?) kids, especially
the ones who are getting bored or frustrated in their mathematics lessons.

I especially intend to insert tuning (not just the most rudimentary
"acoustics"), and whatever could work out of that into a multicultural
thrust (ie non-western music!), without being just silly or kind of
patronizing (as a lot of what I've seen along those lines).

[Yahya]
For some simple maths using ratios, why not explore the history of the
monochord in Ancient Greece? Unless I'm mistaken, we (collectively)
now know much more about actual Hellenic practice than Helmholtz did.

For something possibly less contentious, you could get them to make
panpipes, perhaps using modern Peruvian instruments as models; or
even willow-bark flutes - an old standby of "Things to Make and Do"
books written for the youth of the British Empire in its last days!

The maths of pipes, is to first approximation very similar to that of
strings, as I'm sure you know, so you could use either pipes or strings
to explore tuning by ratios.

With the monochord, you can also explore the relation of pitch to
tension - given by a weight suspended from the free end.

You may have seen the recent discussion on the Harmonograph, or
double pendulum. Using a simple pendulum gives some fun physical
maths. And your pendulum and weight could come from turning
your horizontal monochord to stand upright! Simple and inexpensive
apparatus can be improvised to serve these dual purposes.

So what of the double pendulum? I've wondered idly whether
there is a good way to "lay it flat" to produce a musical instrument
with two tunable lengths ... let me know if you have any ideas!

________________________________________________________________________

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Pete,

I'll try to answer your questions, and maybe others will chime in
with something useful for your purposes.

1.) "When and how (!) did the relationship of music to numbers-or vice
versa- become meaningful to you?" (if it did... :-)

[Yahya]
Hearing the difference between the Chopin Waltzes and
Schubert Marches my mother played on the piano, at an early age,
I asked her why they sounded so different. That's when I learnt
about counting 3- and 4-beat metres, and was the first intimation
that number had to do with music.

2.) "As a mathematically or technically inclined person, what, if anything,
have you felt to be an unfortunate oversight in your musical education?"

[Yahya]
Because I was deemed smart enough for science and maths, I was
"streamed" into a group that had less "arts" material. That meant
that I only studied music for two years in high school, which was
a bitter disappointment. But it didn't stop me learning! :-)

*And* the reverse of that,

3.) "As a musically inclined person, ...in your mathematical/technical
education?"

[Yahya]
Not enough application of physical science and maths to music!
For example, I would love to have known sooner about the
structural differences in the timbres of various instruments,
and timbre's connection to spectral analysis.

(Similarly, the colour and composition theory they taught us in art
would have benefitted greatly from a small dose of maths ... .)

You also wrote -
[Pete]
But, I'm really trying to address issues of creativity and
individuality/originality, so as to encourage both as means to better
overall education.

[Yahya]
I've actually found simple maths - counting! - of most application
to my music-making in these two areas -

a. Choice or construction of metres. I use a few with irregular
accents, not suited to western 2/4, 3/4, 4/4 dance, so I'm
possibly more attuned to their possiblities than many when
they crop up in a short improvised tune. I've long enjoyed the
rhythms of Chinese tone-song - based on poetic speech, not
dance; and also classical Indian _tala_. One of my favourite
compositional devices is polyrhythm.

b. Choice of simplified scales. By limiting the tonal resources,
I feel we can enhance our expressive capabilities; I'd go so far
as to say that many musicians would be unable to create music
that is interesting and listenable if they didn't have the 12-tone
chromatic scale to fall back on. Accordingly, I've usually made
it my discipline to limit the number of scale degrees I use in any
piece to the notes of the [heptatonic] diatonic scale, often many
fewer.

I recently performed a work-in-progress using a new
(to me) pentatonic scale - C D Eb G Bb, which gives quite novel
harmonic progressions using both parallel and contrary motion.
In this scale, G is the fourth scale degree, not the fifth; and Bb
is the fifth, not the seventh. So proceeding by "thirds" or
"fifths" introduces a lot of colour. Of course, this scale is NOT
diatonic, as it has four different step sizes, of about
2, 1, 4, 3 [and 2] semitones. I'm sure there are many new scales
waiting to be selected from even the most basic gamut. Mind
you, I didn't count the steps until I'd already improvised on
these notes; counting only serves to explain _why_ this scale is
unusual.

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Sat, 12 Mar 2005 12:35:08 -0800 (PST)
From: Pete McRae <ambassadorbob@yahoo.com>
Subject: Re: A Young Person's Guide to Music and Number

Thanks, Yahya,

It's always good to get a rethink of what I'm after.

I only skimmed the harmonograph thread, but I'll look at it again.

The audience I intend to address (for now) would hopefully be a
cross-section of teaching professionals (from as many fields as I could
entice with a catchy title, which is not the subject line here!),
psychologists/counselors, etc. and university students. My experience has
been that it's the singers who are the most recalcitrant when it comes to
theory, and especially math. ;-) (Sorry...)

Better questions to you and the group, for my purposes, might be,

1.) "When and how (!) did the relationship of music to numbers-or vice
versa- become meaningful to you?" (if it did... :-)

2.) "As a mathematically or technically inclined person, what, if anything,
have you felt to be an unfortunate oversight in your musical education?"

Or the reverse of that,

3.) "As a musically inclined person, ...in your mathematical/technical
education?"

Many of the American students I've observed in World Music classes find the
music of other cultures "irritating" or "boring", especially the further one
gets from any kind of western pop-music "fusion". (My own feelings are
pretty much the opposite, the less like western music it sounds, the happier
I am to listen to it! So to speak...)

In any case, it seems to me that early exposure to different musical
practices would help to make it easier for an opera singer to listen to
Indian classical music, for example. (Or, in my case, for rock 'n' roller
to listen to, say, Schubert.)

But, I'm really trying to address issues of creativity and
individuality/originality, so as to encourage both as means to better
overall education. In the present educational environment [in California,
at least] I think a large scale disaster is most often frightfully
exacerbated by official policy.

Of course, this may only be my unfortunate opinion, and in fact the system
will be wildly successful, once _all_ artistic considerations are weeded
out.

;-)

Regards,

Pete

Yahya Abdal-Aziz <yahya@melbpc.org.au> wrote:

-----Original
Message-----________________________________________________________________
________
Date: Fri, 11 Mar 2005 00:24:29 -0800 (PST)
From: Pete McRae
Subject: Re: A Young Person's Guide to Music and Number (was CD Sales...)

...

[Pete]
I'm presently really trying hard to brainstorm a Senior Project for a Music
Ed. degree, that could take a more rigorous (?) pedagogical approach to
music and number, for high school (and elementary school?) kids, especially
the ones who are getting bored or frustrated in their mathematics lessons.

I especially intend to insert tuning (not just the most rudimentary
"acoustics"), and whatever could work out of that into a multicultural
thrust (ie non-western music!), without being just silly or kind of
patronizing (as a lot of what I've seen along those lines).

[Yahya]
For some simple maths using ratios, why not explore the history of the
monochord in Ancient Greece? Unless I'm mistaken, we (collectively)
now know much more about actual Hellenic practice than Helmholtz did.

For something possibly less contentious, you could get them to make
panpipes, perhaps using modern Peruvian instruments as models; or
even willow-bark flutes - an old standby of "Things to Make and Do"
books written for the youth of the British Empire in its last days!

The maths of pipes, is to first approximation very similar to that of
strings, as I'm sure you know, so you could use either pipes or strings
to explore tuning by ratios.

With the monochord, you can also explore the relation of pitch to
tension - given by a weight suspended from the free end.

You may have seen the recent discussion on the Harmonograph, or
double pendulum. Using a simple pendulum gives some fun physical
maths. And your pendulum and weight could come from turning
your horizontal monochord to stand upright! Simple and inexpensive
apparatus can be improvised to serve these dual purposes.

So what of the double pendulum? I've wondered idly whether
there is a good way to "lay it flat" to produce a musical instrument
with two tunable lengths ... let me know if you have any ideas!

________________________________________________________________________

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.308 / Virus Database: 266.7.2 - Release Date: 11/3/05

Thanks, Yahya, for a wonderfully generous reply!

P

Yahya Abdal-Aziz <yahya@melbpc.org.au> wrote:

Pete,

I'll try to answer your questions, and maybe others will chime in
with something useful for your purposes.

1.) "When and how (!) did the relationship of music to numbers-or vice
versa- become meaningful to you?" (if it did... :-)

[Yahya]
Hearing the difference between the Chopin Waltzes and
Schubert Marches my mother played on the piano, at an early age,
I asked her why they sounded so different. That's when I learnt
about counting 3- and 4-beat metres, and was the first intimation
that number had to do with music.

2.) "As a mathematically or technically inclined person, what, if anything,
have you felt to be an unfortunate oversight in your musical education?"

[Yahya]
Because I was deemed smart enough for science and maths, I was
"streamed" into a group that had less "arts" material. That meant
that I only studied music for two years in high school, which was
a bitter disappointment. But it didn't stop me learning! :-)

*And* the reverse of that,

3.) "As a musically inclined person, ...in your mathematical/technical
education?"

[Yahya]
Not enough application of physical science and maths to music!
For example, I would love to have known sooner about the
structural differences in the timbres of various instruments,
and timbre's connection to spectral analysis.

(Similarly, the colour and composition theory they taught us in art
would have benefitted greatly from a small dose of maths ... .)

You also wrote -
[Pete]
But, I'm really trying to address issues of creativity and
individuality/originality, so as to encourage both as means to better
overall education.

[Yahya]
I've actually found simple maths - counting! - of most application
to my music-making in these two areas -

a. Choice or construction of metres. I use a few with irregular
accents, not suited to western 2/4, 3/4, 4/4 dance, so I'm
possibly more attuned to their possiblities than many when
they crop up in a short improvised tune. I've long enjoyed the
rhythms of Chinese tone-song - based on poetic speech, not
dance; and also classical Indian _tala_. One of my favourite
compositional devices is polyrhythm.

b. Choice of simplified scales. By limiting the tonal resources,
I feel we can enhance our expressive capabilities; I'd go so far
as to say that many musicians would be unable to create music
that is interesting and listenable if they didn't have the 12-tone
chromatic scale to fall back on. Accordingly, I've usually made
it my discipline to limit the number of scale degrees I use in any
piece to the notes of the [heptatonic] diatonic scale, often many
fewer.

I recently performed a work-in-progress using a new
(to me) pentatonic scale - C D Eb G Bb, which gives quite novel
harmonic progressions using both parallel and contrary motion.
In this scale, G is the fourth scale degree, not the fifth; and Bb
is the fifth, not the seventh. So proceeding by "thirds" or
"fifths" introduces a lot of colour. Of course, this scale is NOT
diatonic, as it has four different step sizes, of about
2, 1, 4, 3 [and 2] semitones. I'm sure there are many new scales
waiting to be selected from even the most basic gamut. Mind
you, I didn't count the steps until I'd already improvised on
these notes; counting only serves to explain _why_ this scale is
unusual.

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Sat, 12 Mar 2005 12:35:08 -0800 (PST)
From: Pete McRae
Subject: Re: A Young Person's Guide to Music and Number

Thanks, Yahya,

It's always good to get a rethink of what I'm after.

I only skimmed the harmonograph thread, but I'll look at it again.

The audience I intend to address (for now) would hopefully be a
cross-section of teaching professionals (from as many fields as I could
entice with a catchy title, which is not the subject line here!),
psychologists/counselors, etc. and university students. My experience has
been that it's the singers who are the most recalcitrant when it comes to
theory, and especially math. ;-) (Sorry...)

Better questions to you and the group, for my purposes, might be,

1.) "When and how (!) did the relationship of music to numbers-or vice
versa- become meaningful to you?" (if it did... :-)

2.) "As a mathematically or technically inclined person, what, if anything,
have you felt to be an unfortunate oversight in your musical education?"

Or the reverse of that,

3.) "As a musically inclined person, ...in your mathematical/technical
education?"

Many of the American students I've observed in World Music classes find the
music of other cultures "irritating" or "boring", especially the further one
gets from any kind of western pop-music "fusion". (My own feelings are
pretty much the opposite, the less like western music it sounds, the happier
I am to listen to it! So to speak...)

In any case, it seems to me that early exposure to different musical
practices would help to make it easier for an opera singer to listen to
Indian classical music, for example. (Or, in my case, for rock 'n' roller
to listen to, say, Schubert.)

But, I'm really trying to address issues of creativity and
individuality/originality, so as to encourage both as means to better
overall education. In the present educational environment [in California,
at least] I think a large scale disaster is most often frightfully
exacerbated by official policy.

Of course, this may only be my unfortunate opinion, and in fact the system
will be wildly successful, once _all_ artistic considerations are weeded
out.

;-)

Regards,

Pete

Yahya Abdal-Aziz wrote:

-----Original
Message-----________________________________________________________________
________
Date: Fri, 11 Mar 2005 00:24:29 -0800 (PST)
From: Pete McRae
Subject: Re: A Young Person's Guide to Music and Number (was CD Sales...)

...

[Pete]
I'm presently really trying hard to brainstorm a Senior Project for a Music
Ed. degree, that could take a more rigorous (?) pedagogical approach to
music and number, for high school (and elementary school?) kids, especially
the ones who are getting bored or frustrated in their mathematics lessons.

I especially intend to insert tuning (not just the most rudimentary
"acoustics"), and whatever could work out of that into a multicultural
thrust (ie non-western music!), without being just silly or kind of
patronizing (as a lot of what I've seen along those lines).

[Yahya]
For some simple maths using ratios, why not explore the history of the
monochord in Ancient Greece? Unless I'm mistaken, we (collectively)
now know much more about actual Hellenic practice than Helmholtz did.

For something possibly less contentious, you could get them to make
panpipes, perhaps using modern Peruvian instruments as models; or
even willow-bark flutes - an old standby of "Things to Make and Do"
books written for the youth of the British Empire in its last days!

The maths of pipes, is to first approximation very similar to that of
strings, as I'm sure you know, so you could use either pipes or strings
to explore tuning by ratios.

With the monochord, you can also explore the relation of pitch to
tension - given by a weight suspended from the free end.

You may have seen the recent discussion on the Harmonograph, or
double pendulum. Using a simple pendulum gives some fun physical
maths. And your pendulum and weight could come from turning
your horizontal monochord to stand upright! Simple and inexpensive
apparatus can be improvised to serve these dual purposes.

So what of the double pendulum? I've wondered idly whether
there is a good way to "lay it flat" to produce a musical instrument
with two tunable lengths ... let me know if you have any ideas!

________________________________________________________________________

--
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Pete,

Let's all share :-)

BTW, was it you who had a crack at our members for not
composing good music? Couldn't be ... you're too nice!

I'd recommend a certain piece called "Imaginary Horses"
for at least _two_ listenings before you write us all off!

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Tue, 15 Mar 2005 03:42:27 -0800 (PST)
From: Pete McRae <ambassadorbob@yahoo.com>
Subject: Re: Re: A Young Person's Guide to Music and Number

Thanks, Yahya, for a wonderfully generous reply!

P

...

________________________________________________________________________
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Checked by AVG Anti-Virus.
Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 15/3/05

Yahya,

Um, I once earned the nickname 'Rattlesnake' from the guys in a rock band...that I was with for about...5 years...Man, did _they_ ever suck?! ;-)

Seriously, if I got a bunch of replies like yours, I'd have the makings of a nice little "study"! I've got plenty to go on as it is, but the personal biography is much (triple underline) appreciated!

(If anyone reading this would like to contact me off-list, that would be great, too!)

Where can I hear that piece?

Best,

Pete

Yahya Abdal-Aziz <yahya@melbpc.org.au> wrote:

Pete,

Let's all share :-)

BTW, was it you who had a crack at our members for not
composing good music? Couldn't be ... you're too nice!

I'd recommend a certain piece called "Imaginary Horses"
for at least _two_ listenings before you write us all off!

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Tue, 15 Mar 2005 03:42:27 -0800 (PST)
From: Pete McRae
Subject: Re: Re: A Young Person's Guide to Music and Number

Thanks, Yahya, for a wonderfully generous reply!

P

...

________________________________________________________________________
--
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Checked by AVG Anti-Virus.
Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 15/3/05

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
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---------------------------------
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Yahoo! Small Business - Try our new resources site!

PS

Was it Cantor or Dedekind who actually wrote _The Structure of
Atonal Music_?

Cheers,

P

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> Pete,
>
> Let's all share :-)
>
> BTW, was it you who had a crack at our members for not
> composing good music? Couldn't be ... you're too nice!
>
> I'd recommend a certain piece called "Imaginary Horses"
> for at least _two_ listenings before you write us all off!
>
> Regards,
> Yahya
>
>
> -----Original Message-----
>
_____________________________________________________________________
___
> Date: Tue, 15 Mar 2005 03:42:27 -0800 (PST)
> From: Pete McRae <ambassadorbob@y...>
> Subject: Re: Re: A Young Person's Guide to Music and Number
>
> Thanks, Yahya, for a wonderfully generous reply!
>
> P
>
> ...
>
>
_____________________________________________________________________
___
> --
> No virus found in this outgoing message.
> Checked by AVG Anti-Virus.
> Version: 7.0.308 / Virus Database: 266.7.3 - Release Date: 15/3/05